charge balance
Any solution you can pour out of a beaker is electrically neutral overall — it does not zap your hand. That simple fact has a powerful accounting consequence: somewhere in the liquid, all the positive charges must add up to exactly the same total as all the negative charges. Writing that balance down explicitly is the charge balance equation.
Concretely, you sum the concentration of every positive ion, each weighted by how many charges it carries, and set that equal to the same weighted sum for every negative ion. A doubly charged ion counts double, because it brings two charges to the tally. This is not an approximation; it is an exact law that every solution obeys, rooted in the principle of electroneutrality.
The charge balance is one of the three pillars of the systematic treatment of equilibrium, supplying an essential equation that links the unknown concentrations together. Its honest limitation is that it is just one equation, and it does not on its own say how much of anything there is — it only constrains the ions to be in electrical step. You still need the mass balances and the equilibrium constants to pin down actual concentrations.
For a solution of sodium carbonate in water, the charge balance reads: [Na+] + [H+] = [OH-] + [HCO3-] + 2[CO3^2-] — note the doubly charged carbonate is multiplied by 2.
Multiply each ion's concentration by its charge before summing.
A frequent slip is forgetting the charge multiplier. The coefficient in a charge balance comes from the ion's charge (so 2 for a 2- ion), which is different from a mass balance, where coefficients come from how many of that atom are in the formula. The two equations look similar but count different things.